Is it permissible for a husband to leave his wife for three nights to sleep alone, while he sleeps at his mother's in the same house but on a different floor, knowing that there were previous disagreements between the wife and the mother?

There is no objection to the husband staying with his mother for three nights and with his wife for one night, because he is not obliged to stay with his wife every night. Jurists have differed regarding the obligation of a husband staying overnight with his wife:

Hanafi and Hanbali schools: They believe that staying overnight is obligatory. However, the Hanafis did not specify a duration, while the Hanbalis believe that one night every four nights is obligatory, based on the story of Ka'b ibn Suwar with Umar ibn al-Khattab, may Allah be pleased with him.

Maliki and Shafi'i schools: They believe that staying overnight is recommended and not obligatory. The Shafi'is said that the minimum degree of Sunnah is one night every four nights.